Mathematical methods for the natural and engineering sciences

• 作者: Mickens, Ronald E.,
• 出版: [River Edge, N.J.] : World Scientific ©2004.
• 稽核項: 1 online resource (xxi, 509 pages) :illustrations.
• 叢書名: Series on advances in mathematics for applied sciences ;v. 65
• 標題: Mathematical analysis. , MATHEMATICS Mathematical Analysis. , MATHEMATICS Calculus. , Mathematical Analysis. , Electronic books. , MATHEMATICS , Analyse mathématique. , Calculus.
• ISBN: 9812387501 , 9789812387509
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• 附註: Includes bibliographical references and index. Intro; Mathematical Methods for the Natural and Engineering Sciences; Contents; 1. Introduction; 1.1 Mathematical Modeling; 1.2 Mathematical versus Physical Equations; 1.3 Dimensionless Variables and Characteristic Scales; 1.4 Construction of Mathematical Equations; 1.4.1 Decay Equation; 1.4.2 Logistic Equation; 1.4.3 The Fisher Equation; 1.4.4 Duffingsâ#x80;#x99; Equation; 1.4.5 Budworm Population Dynamics; 1.5 Nonlinearity; Problems; Comments and References; Bibliography; Dimensionless Variables and Scaling; Mathematical Modeling; Nonlinearity; 2. Trigonometric Relations and Fourier Analysis 2.8.1 Definition of Fourier Transforms2.8.2 Basic Properties of Fourier Transforms; 2.9 Application of Fourier Transforms; 2.9.1 Fourier Transform of the Square Pulse; 2.9.2 Fourier Transform of the Gaussian Function; 2.9.3 The Convolution Theorem; 2.9.4 The Diffusion Equation; 2.9.5 The Wave Equation; 2.10 The Laplace Transform; Linearity Condition; Shift Theorems; Scaling Condition; Differentiation of a Transform; Transform of an Integral; Integration of the Transform; Transform of Derivatives; Convolution Theorem; Transform of a Periodic Function 2.11 Worked Problems Using the Laplace Transform2.11.1 Laplace Transform of t-1/3; 2.11.2 The Square Wave Function; 2.11.3 The Dirac Delta Function; Problems; Comments and References; Bibliography; 3. Gamma, Beta, Zeta, and Other Named Functions; 3.1 Scope of Chapter; 3.2 Gamma Function; 3.3 The Beta Function; 3.4 The Riemann Zeta Function; 3.5 The Dirac Delta Function; 3.6 Dirichlet Integrals; 3.7 Applications; 3.7.1 Additional Properties of (z); 3.7.2 A Definite Integral Containing Logarithms; 3.7.3 A Class of Important Integrals; 3.7.4 A Representation for x-p 3.7.5 Additional Properties of the Beta Function3.7.6 Fermi-Dirac Integrals; 3.7.7 An Integral Involving an Exponential; 3.7.8 Fermi-Dirac Integrals Containing Logarithms; 3.7.9 Magnetic Moment of the Electron; 3.7.10 Relationship Between the Theta and Delta Functions; 3.7.11 Evaluation of Integrals by Use of the Beta Function; 3.8 Other Named Functions; 3.9 Elliptic Integrals and Functions; 3.9.1 Elliptic Integrals of the First and Second Kind; 3.9.2 Jacobi Elliptic Functions; 3.10 Evaluation of Integrals; Problems; Comments and References; Bibliography
• 摘要: This book provides a variety of methods required for the analysis andsolution of equations which arise in the modeling of phenomena fromthe natural and engineering sciences. It can be used productively byboth undergraduate and graduate students, as well as others who needto learn and understand these techniques. A detailed discussion isalso presented for several topics that are usually not included instandard textbooks at this level: qualitative methods for differentialequations, dimensionalization and scaling, elements of asymptotics, difference equations, and various perturbation methods. Eac.
• 電子資源: https://dbs.tnua.edu.tw/login?url=https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=130030
• 系統號: 005317177
• 資料類型: 電子書
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• 引用網址: 複製連結
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